{"title":"Neostability transfers in derivation-like theories","authors":"Omar Leon Sanchez, Shezad Mohamed","doi":"arxiv-2409.11248","DOIUrl":null,"url":null,"abstract":"Motivated by structural properties of differential field extensions, we\nintroduce the notion of a theory $T$ being derivation-like with respect to\nanother model-complete theory $T_0$. We prove that when $T$ admits a\nmodel-companion $T_+$, then several model-theoretic properties transfer from\n$T_0$ to $T_+$. These properties include completeness, quantifier-elimination,\nstability, simplicity, and NSOP$_1$. We also observe that, aside from the\ntheory of differential fields, examples of derivation-like theories are\nplentiful.","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11248","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Motivated by structural properties of differential field extensions, we
introduce the notion of a theory $T$ being derivation-like with respect to
another model-complete theory $T_0$. We prove that when $T$ admits a
model-companion $T_+$, then several model-theoretic properties transfer from
$T_0$ to $T_+$. These properties include completeness, quantifier-elimination,
stability, simplicity, and NSOP$_1$. We also observe that, aside from the
theory of differential fields, examples of derivation-like theories are
plentiful.
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